Login/Sign Up
Home » Find the number of integers greater than 7000 that can be formed with the digits 3, 5, 7, 8 and 9 where no digits are repeated. [Hint: Besides 4-digit integers greater than 7000, five digit integers are always greater than 7000.]
Find the number of integers greater than 7000 that can be formed with the digits 3, 5, 7, 8 and 9 where no digits are repeated. [Hint: Besides 4-digit integers greater than 7000, five digit integers are always greater than 7000.]
CBSE | Class 11 | Maths | NCERT Exemplar | Permutations and Combinations
Find the number of integers greater than 7000 that can be formed with the digits 3, 5, 7, 8 and 9 where no digits are repeated. [Hint: Besides 4-digit integers greater than 7000, five digit integers are always greater than 7000.]

Solution:

As per the question,

The digits that can be used =3,5,7,8,9

As, no digits can be repeated,

No. of integers is { }^{5} \mathrm{P}_{5}=5 !=120

For a 4 digit integer to be greater than 7000 ,

The 4 digit integer should begin with 7,8 or 9 .

The no. of such integer =3 \times{ }^{4} \mathrm{P}_{3}=3 \times{ }^{4} \mathrm{P}_{3}=3(24)=72

As a result, the total number of ways =120+72=192

i

More Material